With any irreducible root system \(\Phi \)  Steinberg [1]}, [2]} associated the so-called Steinberg group,
which is an extension of the simple complex algebraic group of type \(\Phi \) .
Later Stein [3]} extended Steinberg's construction over any commutative ring \(R\) ,
thus leading to the Steinberg group \(\operatorname{St}(\Phi ,R)\) .
We are interested in the case when the root system \(\Phi \)  is of type \(C_n\)  (\(n\ge 2\) ) and \(R = {\mathbb {Z}}\)  is the ring
of integers. The corresponding Steinberg group \(\operatorname{St}(C_n,{\mathbb {Z}})\)  is an extension of the symplectic modular group \(\operatorname{Sp}_{2n}({\mathbb {Z}})\) .
